Download Making Sense of Effective Bits in Oscilloscope Measurements

Technical Brief
Making Sense of Effective Bits
in Oscilloscope Measurements
When considering oscilloscope or digitizer performance, the term “Effective Number
of Bits” (ENOB or effective bits) is often used, but it seems seldom fully appreciated
or understood, especially in terms of what it means to real-world signals and
measurements. In this paper, we will describe effective bits in terms that are useful
in better understanding the real world implications.
Making Sense of Effective Bits in Oscilloscope Measurements
Technical Brief
Figure 1. Digitizer Errors Contributing to ENOB (courtesy of datatranslation.com).
Effective bits provides a representation of the signal integrity
(or degradation) of the A/D system over a frequency range.
To better understand this, let’s first consider a few basic points.
1. All digitizing systems have a variety of errors that impact the
reported value of voltage at a particular instance in time.
2. All errors, both amplitude and timing related, show up as a
change to the expected or “ideal” voltage at a particular time.
3. In an ideal digitizer, the number of effective bits would
be the same as the resolution of the A/D (e.g., 8 bits),
and this would be consistent from DC to the maximum
bandwidth of the instrument. In reality, all instruments are
less than ideal. The ENOB is usually lower than the
resolution of the A/D, and this usually gets worse as the
frequency is increased.
4. To compare any two A/D systems, it is critical that the
same conditions are used to characterize the performance.
The same stimulus must be used, and the same settings
must be used for the instruments being evaluated.
It should be noted that ENOB is defined by the IEEE1057
specification. In addition, the IEEE1057 specification
describes how to make ENOB measurements. ENOB is an
industry-wide accepted method for determining a general
figure of merit for A/D converters, oscilloscopes, and other
digitizing systems.
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Figure 2. Typical A/D Errors.
Errors in Digitizing Systems
Numerous papers have been written to describe the typical
errors that exist in digitizing systems. An excellent reference
paper is “Effective Bits Testing Evaluates Dynamic
Performance of Digitizing Instruments” and is available at:
http://www2.tek.com/cmsreplive/tirep/4405/2006.07.18.14.
07.40_4405_EN.pdf
Figure 1 shows examples of some of the common errors
which affect ENOB performance in A/D systems.
Effective bits is a composite figure of merit, which includes
the effects of digitizing errors shown in Figure 1 and 2.
Most importantly, it represents these errors as a function of
frequency, so that you can see if a particular instrument has
performance issues at specific frequencies. It should be
noted that the ENOBs calculation is based on all spectral
components, excluding DC, so of the typical errors show
in Figure 2, effective bits is not affected by offset error
(a DC effect).
Making Sense of Effective Bits in Oscilloscope Measurements
Technical Brief
Table 2. Effective Bits Resolution of Tektronix DPO/DSA70000B Oscilloscopes.
Table 1. Digitizer Resolution.
Digitizing Resolution
If a digitizing system has 8 bits of resolution at DC, it has
256 digitizing levels. This means that the input signal must
change at least .39% of the full scale in order for the A/D to
produce a change in its output. If we had a 1V full-scale
range on the 8-bit A/D, the voltage would have to change
by more than 3.9mV to have an impact on the output of the
A/D. Any changes on the input signal lower than 3.9mV
increments would not be detected by the A/D.
Now consider if the resolution is reduced. For example, if
the resolution is reduced to 6.65 bits, the input signal must
change by approximately 1% to produce a change on the
A/D output. Any changes in the input signal that are below
that level will be unseen in the output of the A/D. At a 1V
full-scale range, a change larger than 10mV would be
required to affect the output of the A/D.
Likewise, a resolution of 5 bits provides 32 digitizing levels.
In this situation, the input signal must change by at least
3.13% in order to have any impact on the output of the
A/D. If we once again consider our 1V full-scale range,
it would take a change on the input signal larger than
31.3mV to affect a change on the output of the A/D, as
Table 1 illustrates.
Effective Number of Bits
The effective number of bits is generally presented as a
function of frequency, and generally (but not always) degrades
as the frequency gets higher. This change in resolution
works much like the discussion on digitizing resolution.
Let’s consider the situation where we have an 8-bit realtime oscilloscope. This oscilloscope has 8 bits of resolution
and a bandwidth of 13 GHz. At DC and low frequency, we
Figure 3. Effective Bits plot for DPO70000B at 100mV/div.
will likely have very close to 8 effective bits of resolution.
However, as the frequency of the input signal being measured increases, the impact of instrument noise and other
errors will likely degrade the effective bits performance.
Figure 3 shows the plot of effective bits for such an instrument.
Figure 3 shows the performance of a Tektronix
DPO/DSA70000B oscilloscope over the range from 200 MHz
to 13 GHz. As you can see, at 200 MHz the instrument has
6.4 effective bits of resolution. As the frequency increases,
this drops down to 5.6 effective bits at 13 GHz.
The behavior of the A/D is much the same for effective
bits as it is for “real bits” as described in the “Digitizing
Resolution” section above. Table 2 shows the resolution
details for these effective bits levels.
This shows that at 13 GHz, with a 1V full-scale range, the
input signal will have a 20mV noise content on the output of
the A/D. Said another way, any input signal change smaller
than 20mV will likely be masked by the noise, distortion, and
other errors in the system.
It might be worth noting here that the A/D will continue to
put out 8-bit data, but (at 13 GHz) 2.4 bits of that will
actually be noise/distortion/error.
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Making Sense of Effective Bits in Oscilloscope Measurements
Technical Brief
Table 3. Effective Bits Resolution of Agilent DSO90000 Oscilloscope.
Figure 4. Effective Bits Comparison of Two Real-time Oscilloscopes.
Not All Digitizing Systems Are
Created Equal
After inspecting the effective bits plot of the DPO/DSA70000B
oscilloscopes in Figure 3, you might be wondering if this
represents good performance or poor performance. First,
be assured that it is no easy task to design a system that
performs equally well from DC all the way to 13 GHz, 16 GHz,
or even 20 GHz. No system is perfect, and it should be
expected that some degradation of performance would occur
over the frequency range, even for the finest of instruments.
Having said that, some instruments are better than others,
and the effective bits performance provides at a glance a
very good representation of signal integrity of the digitizing
system, for a specific setting, over its entire frequency
range. The Figure 4 effective bits chart shows a comparison
of the DPO/DSA70000B oscilloscope to a competitive
oscilloscope with similar specifications.
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Note that the Tektronix oscilloscope has the same range of
6.4 down to approximately 5.6 effective bits of resolution for
this setting (400mV full scale) as we saw in the previous
graph (1V full scale), while the competitive oscilloscope
shows a range of 5.9 down to 4 effective bits of resolution.
Table 3 shows the details of the competitive oscilloscope's
effective bits level.
As you can see, at 4 effective bits, there will be a noise
content due to the instrument of 62.5mV for a range of
1V full-scale.
The Relationship Between Signal-toNoise, SINAD, and Effective Bits
As already described, effective bits gives a representation
of noise and other errors in a digitizing system. IEEE-1241
and IEEE-1057 standards give formulas for calculating
effective bits. These standards link signal-to-noise and
distortion (SINAD) performance to effective bits, through
the following equation:
It is clear from this formula that effective bits performance
depends on the signal-to-noise ratio, as well as the
distortion effects.
Making Sense of Effective Bits in Oscilloscope Measurements
Technical Brief
Figure 5. Baseline Noise Measurement.
Figure 6. Baseline Noise Comparison Between the Tektronix DPO70000B and the
Agilent DSO90000A.
Baseline Noise - Not a Good
Representation of ENOB Performance
Baseline noise (sometimes called residual noise) is a representation of the instrument noise performance, measured
without an external signal applied to the input (input grounded).
The measurement is performed using an AC RMS measurement on the channel, or applying a vertical histogram on the
scope trace to accomplish the same end result. It is a quick
and convenient measurement to make, since it doesn’t
require a stimulus signal, but cannot tell you anything about
the performance at a specific frequency. Because it doesn’t
make any representation of instrument noise under the
dynamic conditions of an AC signal at a given frequency
using a substantial range of the A/D, it doesn’t really provide
a good indication of signal integrity in the instrument.
Having said that, some instrument vendors try to use baseline noise to demonstrate the “quality” of their acquisition
system. In these cases, they specify vertical noise as a
voltage level at a particular volts/div setting. In comparing
instruments, however, it is important to compare “% of Full
Scale” to get a fair comparison, since not all instruments
have the same full scale range for a particular volts/div
setting. It is also important to have the bandwidth set the
same when comparing the performance of two different
instruments. Higher bandwidth instruments intrinsically
have more noise, and setting the bandwidth limit will reduce
the noise.
noise. Once this is attained, it is a simple matter of calculating
the % of full scale for the particular setting being used. Some
systems provide a built-in math function that measures AC RMS
directly, without having to set up a histogram manually. It is
important not to include the DC offset in this measurement,
so histograms or AC RMS measurements must be used. The
Figure 5 screen capture shows a baseline noise measurement.
Figure 6 shows a comparison of baseline noise for the
Tektronix DPO70000B and the Agilent DSO90000A. The
bandwidth was limited to 13GHz on the Tektronix instrument
to match the Agilent maximum bandwidth. This plot shows
the baseline noise at many settings, so that it is possible to
see how the baseline noise as a % of full-screen changes
as a function of the volts/div setting. These are the same
two instruments that were compared for effective bits
performance in Figure 4.
You can see from the comparison that the Tektronix instrument
offers the lower baseline noise performance (approximately
10% to 20% lower depending on setting), but compared to
the effective bits results we saw in Tables 2 and 3, this is a
small % of the full scale. The difference here is generally less
than .1% of full scale, whereas the effective bits difference
we saw in Tables 2 and 3 was as much as 4.25% of full
scale. So, as you can see, baseline noise doesn’t really
give the full magnitude of the signal integrity picture. Most
importantly, it doesn’t utilize an actual signal, so it cannot be
related to SNR or ENOB performance.
As stated previously, the measurement is performed using a
vertical histogram on the oscilloscope trace. The standard
deviation of the histogram represents the rms value of the
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Making Sense of Effective Bits in Oscilloscope Measurements
Technical Brief
Figure 7. Side-by-Side Comparison of 6.5 GHz Sinewave on Tektronix and Agilent Oscilloscopes.
How ENOB is Exhibited in
Real-world Signals
Effective bits performance will have an effect on both
amplitude measurements and timing measurements.
The following are discussions on these topics.
ENOB Effects on Amplitude Measurements
Next, let’s consider the acquisition of a sinewave. Again,
we will compare the Tektronix DPO/DSA70000B and
the Agilent DSO90000A instruments to demonstrate
how effective bits performance can be seen in real
world measurements.
In Figure 7 we have applied the same 6.5 GHz sinewave
to both the Tektronix DPO/DSA70000B and the Agilent
DSO90000A oscilloscopes. Both instruments are set for
13 GHz bandwidth, and both instruments are set for
400mV full scale. Both instruments have been set for
infinite display persistence, so that variations across all
acquisitions can be seen. No averaging is applied to
either instrument. Both instruments were run for
approximately 10k acquisitions.
On the Tektronix oscilloscope, we see approximately
15.9mV of trace “thickness” at the peak. This represents
3% of full scale on the Tektronix oscilloscope.
On the Agilent oscilloscope, we see approximately 37mV
of trace “thickness” at the peak. This represents 9% of
full scale on the Agilent oscilloscope.
You can see in Figure 3 that at 6.5 GHz, the Tektronix
oscilloscope is at its lowest effective bits (approximately
5.6 bits), while the Agilent oscilloscope is at approximately
4.5 effective bits.
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Figure 8. Jitter Measurement Comparisons.
ENOB Effects on Jitter Measurements
Jitter (aperture uncertainty and other sources of timing error)
is one of the error elements represented under effective
bits. So, it does not come as much surprise that we can
see real-world effects on jitter measurements. In Figure 8,
the jitter measurements shown were made using a BERT
pattern generator as the signal source, with the data
pattern set to a 1010 pattern. The BERT pattern
generator is a very clean signal generator. For this test,
the pattern generator was set to 5 different data rates,
and jitter measurements performed on each of the
instruments shown.
The Tektronix DPO/DSA70000B demonstrated the
lowest jitter measurement performance for all data rates
measured. While the Agilent 90000A oscilloscope exhibited
26% to 41% higher measured jitter, neither of the instruments varied significantly across the data rates measured.
Making Sense of Effective Bits in Oscilloscope Measurements
Technical Brief
Figure 9. Jitter Noise Floor Test Configuration.
ENOB Effects on Eye Diagrams
Conclusion
As you might expect, ENOB effects can also be seen on
eye diagrams. Both amplitude and jitter on the eye are
impacted by ENOB performance
As we have seen, effective bits is a general figure of merit
for signal integrity in any A/D system, including real-time
oscilloscopes. Effective bits represents the cumulative errors
in a digitizing system across a frequency range, for a fixed
instrument setting. Generally, the effective bits decreases as
frequency increases.
The following are two eye diagrams that were created
using the same BERT pattern generator as a signal
source, with the data rate set at 5Gbps. This is
representative of the signals associated with PCI-E Gen2
and USB 3.0. This signal was applied to the Tektronix
DPO70000B, as well as the Agilent DSO81304. Both
instruments we set as near as possible to the same
settings prior to making measurements. Both instruments were set up to measure TIE Jitter.
From the side-by-side comparison, you can see that
both jitter and amplitude noise are impacted. The
measured jitter using the Tektronix oscilloscope for this
test was 3.08ps pk-pk, whereas the measured jitter
using the Agilent oscilloscope shows 11.4ps pk-pk on
the same signal. The Agilent oscilloscope measured over
350% more jitter for this signal.
Likewise, the amplitude measurements show substantial
differences. In this case, a rough measurement of the
eye height at the 50% point of the eye showed approximately 582mV on the Tektronix oscilloscope, as compared
to approximately 521mV on the Agilent oscilloscope. In
this case, the Agilent oscilloscope measured 10% lower
at the 50% point of the eye.
We have seen that the errors associated with lower effective
bits performance can easily be seen in real-world signals as
increased noise when performing amplitude measurements,
and increased jitter when making jitter measurements.
As the effective bits decreases, the measurement precision
of the instrument decreases. This directly equates to the
margin available for tests being performed on the instrument.
For example, you might find that you are not able to pass
a compliance test for a particular standard because the
instrument being used simply doesn’t have the margin
needed for the test limits that are specified. Instruments
with higher effective bits will produce more repeatable
measurements due to the superior precision of the
measurement system.
Gen2 and Gen3 data rates demand more performance
from the test instrumentation. It is not enough to have
adequate bandwidth on the oscilloscope being used to
make measurements. Excellent ENOB performance is also
required to assure adequate margin on the measurements
being made.
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Updated 30 October 2008
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